Electromagnetic Energy for a Charged Kerr Black Hole in a Uniform Magnetic Field

Abstract

With the Komar mass formula we calculate the electromagnetic energy for a charged Kerr black hole in a uniform magnetic field. We find that the total electromagnetic energy takes the minimum when the Kerr black hole possesses a non-zero net charge $Q = 2ξB_0 J_H$ where $B_0$ is the strength of the magnetic field, $J_H$ is the angular momentum of the black hole, $ξ$ is a dimensionless parameter determined by the spin of the black hole.